Cluster synchronization for directed heterogeneous dynamical networks via decentralized adaptive intermittent pinning control

In this paper, by proposing a novel adaptive intermittent scheme, we consider the intermittent pinning-control problem for cluster synchronization of directed heterogeneous dynamical networks, i.e., directed networks with nonidentical dynamical nodes. Through constructing a piecewise Lyapunov function and utilizing the analysis technique, some sufficient conditions to guarantee global cluster synchronization are derived. It is noted that the adaptive intermittent strategy developed in this paper is decentralized, which only relies on some local information rather than the global information of the whole network. Finally, a numerical example is given to illustrate the effectiveness of the theoretical results.